PASS Scripta Varia 21 - Pontifical Academy of Sciences

HOW TO BECOME SCIENCE – THE CASE OF COSMOLOGY
3. The Beginning of Relativistic Cosmology
The birth of General Relativity was a real breakthrough, and that of relativistic
cosmology a spectacular application of Einstein’s theory to the
biggest physical system conceivable. After years of struggle and several dramatic
months of painful coda, Einstein, in November 1915, finally wrote
down his gravitational field equations. They were his response to the critical
situation in which Newton’s theory of gravity was deeply immersed (crisis
in any of the major physical theories always has an echo in other areas of
science). Some people were aware of this and tried to remedy the situation
by modifying Newton’s law, but only Einstein, owing to his work in special
relativity, was able to see the connection between gravity and the spaciotemporal
framework of physics, and understood that Newton’s gravity
should not be amended but suitably replaced.
Einstein’s answer to the crisis was a piece of art of enormous beauty. Even
if the final act is a sort of illumination, it certainly did not come as deus ex
machina. Einstein was led to it by a chain of almost deductive reasoning, based
on clearly formulated questions of deep physical significance. This does not
mean that sometimes the chain did not need enormous effort to make the
reasoning transparent. To change his ideas into the body of a physical theory
Einstein had to use completely new mathematical theories, known only to
some experts in pure mathematics but foreign to the community of physicists.
As a result, he obtained a set of ten partial differential equations, the richness
of which he was only dimly aware of. It is true that in the compact tensorial
form they look quite innocent, and when applied to various physical situations
they usually simplify to a tractable mathematical form. Only after acquiring
a certain familiarity with them, one can guess their abysmal richness
from the fact that, when applied to different problems, they reveal unexpected
layers of their mathematical structure. If you read in popular books that Einstein’s
equations present the gravitational field as the curvature of a four-dimensional
space-time, it is only a shortcut of a vast empire of mutual
interactions between non-Euclidean (pseudo-Riemannian, in modern parlance)
geometries and various aspects of physical reality.
In 1917 Einstein produced his first cosmological paper. We already know
the beginning of the cosmological constant story. This constant was, so to
speak, enforced upon Einstein by his equations. Some ten years later, when
it turned out that the universe is not static but expands, Einstein proclaimed
the introduction of the cosmological constant ‘the greatest blunder of his
life’. But in proclaiming this, it was Einstein who was wrong, not his equations.
From the mathematical point of view, the most general (and therefore
the most beautiful) form of Einstein’s equations is the one with the cos-
The Scientific Legacy of the 20 th Century
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